On the extremal number of edges in hamiltonian connected graphs

AbstractAssume that n and δ are positive integers with 3≤δ<n. Let hc(n,δ) be the minimum number of edges required to guarantee an n-vertex graph G with minimum degree δ(G)≥δ to be hamiltonian connected. Any n-vertex graph G with δ(G)≥δ is hamiltonian connected if |E(G)|≥hc(n,δ). We prove that hc(n,δ)=C(n−δ+1,2)+δ2−δ+1 if δ≤⌊n+3×(nmod2)6⌋+1, hc(n,δ)=C(n−⌊n2⌋+1,2)+⌊n2⌋2−⌊n2⌋+1 if ⌊n+3×(nmod2)6⌋+1<δ≤⌊n2⌋, and hc(n,δ)=⌈nδ2⌉ if δ>⌊n2⌋

Observation of Magnetic Moments in the Superconducting State of YBa2_2Cu3_3O6.6_{6.6}

Neutron Scattering measurements for YBa$_2$Cu$_3$O$_{6.6}$ have identified small magnetic moments that increase in strength as the temperature is reduced below $T^\ast$ and further increase below $T_c$. An analysis of the data shows the moments are antiferromagnetic between the Cu-O planes with a correlation length of longer than 195 \AA in the $a$-$b$ plane and about 35 \AA along the c-axis. The origin of the moments is unknown, and their properties are discusssed both in terms of Cu spin magnetism and orbital bond currents.Comment: 9 pages, and 4 figure

DBI with Primordial Magnetic Field in the Sky

In this paper, we study the generation of a large scale magnetic field with amplitude of order $\mu$G in an inflationary model which has been introduced in hep-th/0310221. This inflationary model based on existence of a speed limit for inflaton field. Generating a mass for inflaton at scale above the $\phi_{IR}$, breaks the conformal triviality of the Maxwell equation and causes to originate a magnetic field during the inflation. The amplitude strongly depends on the details of reheating stage and also depends on the e-foldings parameter N. We find the amplitude of the primordial magnetic field at decoupling time in this inflationary background using late time behavior of the theory.Comment: 12 pages, no figure, typos correcte

Resummation Methods at Finite Temperature: The Tadpole Way

We examine several resummation methods for computing higher order corrections to the finite temperature effective potential, in the context of a scalar $\phi^4$ theory. We show by explicit calculation to four loops that dressing the propagator, not the vertex, of the one-loop tadpole correctly counts ``daisy'' and ``super-daisy'' diagrams.Comment: 18 pages, LaTeX, CALT-68-1858, HUTP-93-A011, EFI-93-2

Staggered flux and stripes in doped antiferromagnets

We have numerically investigated whether or not a mean-field theory of spin textures generate fictitious flux in the doped two dimensional $t-J$-model. First we consider the properties of uniform systems and then we extend the investigation to include models of striped phases where a fictitious flux is generated in the domain wall providing a possible source for lowering the kinetic energy of the holes. We have compared the energetics of uniform systems with stripes directed along the (10)- and (11)-directions of the lattice, finding that phase-separation generically turns out to be energetically favorable. In addition to the numerical calculations, we present topological arguments relating flux and staggered flux to geometric properties of the spin texture. The calculation is based on a projection of the electron operators of the $t-J$ model into a spin texture with spinless fermions.Comment: RevTex, 19 pages including 20 figure

Axionic D3-D7 Inflation

We study the motion of a D3 brane moving within a Type IIB string vacuum compactified to 4D on K3 x T_2/Z_2 in the presence of D7 and O7 planes. We work within the effective 4D supergravity describing how the mobile D3 interacts with the lightest bulk moduli of the compactification, including the effects of modulus-stabilizing fluxes. We seek inflationary solutions to the resulting equations, performing our search numerically in order to avoid resorting to approximate parameterizations of the low-energy potential. We consider uplifting from D-terms and from the supersymmetry-breaking effects of anti-D3 branes. We find examples of slow-roll inflation (with anti-brane uplifting) with the mobile D3 moving along the toroidal directions, falling towards a D7-O7 stack starting from the antipodal point. The inflaton turns out to be a linear combination of the brane position and the axionic partner of the K3 volume modulus, and the similarity of the potential along the inflaton direction with that of racetrack inflation leads to the prediction n_s \le 0.95 for the spectral index. The slow roll is insensitive to most of the features of the effective superpotential, and requires a one-in-10^4 tuning to ensure that the torus is close to square in shape. We also consider D-term inflation with the D3 close to the attractive D7, but find that for a broad (but not exhaustive) class of parameters the conditions for slow roll tend to destabilize the bulk moduli. In contrast to the axionic case, the best inflationary example of this kind requires the delicate adjustment of potential parameters (much more than the part-per-mille level), and gives inflation only at an inflection point of the potential (and so suffers from additional fine-tuning of initial conditions to avoid an overshoot problem).Comment: 29 pages, 5 figure

DDW Order and its Role in the Phase Diagram of Extended Hubbard Models

We show in a mean-field calculation that phase diagrams remarkably similar to those recently proposed for the cuprates arise in simple microscopic models of interacting electrons near half-filling. The models are extended Hubbard models with nearest neighbor interaction and correlated hopping. The underdoped region of the phase diagram features $d_{{x^2}-{y^2}}$ density-wave (DDW) order. In a certain regime of temperature and doping, DDW order coexists with antiferromagnetic (AF) order. For larger doping, it coexists with $d_{{x^2}-{y^2}}$ superconductivity (DSC). While phase diagrams of this form are robust, they are not inevitable. For other reasonable values of the coupling constants, drastically different phase diagrams are obtained. We comment on implications for the cuprates.Comment: 7 pages, 3 figure

Kahler Moduli Inflation

We show that under general conditions there is at least one natural inflationary direction for the Kahler moduli of type IIB flux compactifications. This requires a Calabi-Yau which has h^{2,1}>h^{1,1}>2 and for which the structure of the scalar potential is as in the recently found exponentially large volume compactifications. We also need - although these conditions may be relaxed - at least one Kahler modulus whose only non-vanishing triple-intersection is with itself and which appears by itself in the non-perturbative superpotential. Slow-roll inflation then occurs without a fine tuning of parameters, evading the eta problem of F-term inflation. In order to obtain COBE-normalised density perturbations, the stabilised volume of the Calabi-Yau must be O(10^5-10^7) in string units, and the inflationary scale M_{infl} ~ 10^{13} GeV. We find a robust model independent prediction for the spectral index of 1 - 2/N_e = 0.960 - 0.967, depending on the number of efoldings.Comment: 17 pages, 1 figure; v2. references adde

Superconductivity and single crystal growth of Ni0:05TaS2

Superconductivity was discovered in a Ni0:05TaS2 single crystal. A Ni0:05TaS2 single crystal was successfully grown via the NaCl/KCl flux method. The obtained lattice constant c of Ni0:05TaS2 is 1.1999 nm, which is significantly smaller than that of 2H-TaS2 (1.208 nm). Electrical resistivity and magnetization measurements reveal that the superconductivity transition temperature of Ni0:05TaS2 is enhanced from 0.8 K (2H-TaS2) to 3.9 K. The charge-density-wave transition of the matrix compound 2H-TaS2 is suppressed in Ni0:05TaS2. The success of Ni0:05TaS2 single crystal growth via a NaCl/KCl flux demonstrates that NaCl/KCl flux method will be a feasible method for single crystal growth of the layered transition metal dichalcogenides.Comment: 13pages, 6 figures, Published in SS

Network patterns and strength of orbital currents in layered cuprates

In a frame of the $t-J-G$ model we derive the microscopical expression for the circulating orbital currents in layered cuprates using the anomalous correlation functions. In agreement with $\mu$-on spin relaxation ($\mu$SR), nuclear quadrupolar resonance (NQR) and inelastic neutron scattering(INS) experiments in YBa$_2$Cu$_3$O$_{6+x}$ we successfully explain the order of magnitude and the monotonous increase of the {\it internal} magnetic fields resulting from these currents upon cooling. However, the jump in the intensity of the magnetic fields at T$_c$ reported recently seems to indicate a non-mean-field feature in the coexistence of current and superconducting states and the deviation of the extended charge density wave vector instability from its commensurate value {\bf Q}$\approx(\pi,\pi$) in accordance with the reported topology of the Fermi surface